Massive data sets can be collected during manufacturing processes and in connection with research and development activities. Manufacturing processes are sometimes categorized as either “batch” manufacturing processes or “continuous” manufacturing processes. In a batch manufacturing process, a series of steps are performed on a set of raw and/or processed materials over a finite duration to produce a product with desired properties. In some batch processes, processing occurs at a single workstation (e.g., a chamber or container) involving one or more process tools (e.g., process tools within the chamber or container). Examples of batch manufacturing processes include semiconductor wafer processing (e.g., wafer processing resulting in a set of chips), pharmaceutical processing (e.g., the process results in an intermediate or final output set of chemicals, compounds or drugs), or biotechnology processing (e.g., the process results in a particular biological fermentation or cell culture process). In contrast, in continuous manufacturing processes, materials are manufactured, processed or produced substantially without interruption.
As an example, in the semiconductor device manufacturing industry, as device geometries shrink to the nanometer scale, complexity in manufacturing processes increases, and process and material specifications become more difficult to meet. For example, a typical process tool used in current semiconductor manufacturing can be described by a set of several thousand process variables. The variables are generally related to physical parameters of the manufacturing process and/or tools used in the manufacturing process. In some cases, of these several thousand variables, several hundred variables are dynamic (e.g., changing in time during the manufacturing process or between manufacturing processes). The dynamic variables (e.g., gas flow, gas pressure, delivered power, current, voltage, and temperature) can change, sometimes non-linearly, based on a variety of factors, including, for example, a specific processing recipe, the particular step or series of steps in the overall sequence of processing steps, errors and faults that occur during the manufacturing process or changes in parameters.
Generally, process variables associated with a manufacturing process can be divided into two different types, X-type variables (also known as X-variables or inputs) and Y-type variables (also known as Y-variables or outputs). X-type variables are indicative of factors, predictors, or indicators and are used to make projections or predictions about the manufacturing process or results of the manufacturing process. Y-type variables are indicative of yields or responses of the manufacturing processes. X-type variables and Y-type variables are generally related to each other. Often, the exact relationship between the X-type variables and Y-type variables is uncertain or difficult or impossible to determine. The relationship can, in some instances, be approximated or modeled by various techniques, such as linear approximation, quadratic approximation, polynomial fitting methods, exponential or power-series relationships, multivariate techniques (e.g., principal component analysis or partial least squares analysis), among others. In such cases, the relationship between X-type variables and Y-type variables can be inferred based on observing changes to one type of variables and observing responses on the other type of variables.
In a manufacturing process, it is important to be able to predict future behavior of process variables in real time or in near real time as the process progresses, but before the process is completed. Predicted process behavior can have many applications, one of which is to monitor the future trajectories of critical process parameters. For example, in biological manufacturing, early warnings of toxin production, nutrient levels, growth kinetics and other cell performance metrics can be used to make corrective decisions for steering the process to improve yield or provide consistent quality. Another application is to provide an estimate of the yield of the process before it is completed, which can be used to induce proactive modifications to the process or downstream operations. For example, in biological manufacturing, early detection of a low yield can be used as a basis for making adjustments to the process recipe to account for variations in cell performance (e.g., variations in growth rate). In general, based on estimated future behavior of process variables, an operator can have advanced warnings of potential deviations and faults and develop avoidance strategies accordingly during process execution.
There are several existing approaches for predicting the future behavior of a manufacturing process. For example, when a batch process is partially completed, imputation methods can be used to estimate the future trajectories of process variables. Using imputation, estimated future trajectory of a manufacturing process can be determined based on measured historical values of various process variables. However, existing imputation approaches are iterative in nature and often take many iterations before convergence to a fairly accurate prediction.